Concept explainers
Each of the gears A and B has a mass of 10 kg and a radius of gyration of 190 mm, while gear C has a mass of 2.5 kg and a radius of gyration of 80 mm. If a couple M of constant magnitude 6 N
(a)
Number of revolutions of gear C.
Answer to Problem 17.11P
Number of revolutions of gear C is
Explanation of Solution
Given information:
Mass of the gear A (mA) = 10kg.
Radius of gyration of the gear A (kA) = 190mm.
Mass of the gear B (mB) = 10kg.
Radius of gyration of the gear B (kB) = 190mm.
Mass of the gear C (mC) = 2.5kg.
Radius of gyration of the gear C (kC) = 80mm.
Initial angular velocity of gear C (NC)1 = 450rpm
Final angular velocity of gear C (NC)1 = 1800rpm
A couple at gear C (M) = 6N-m.
Radius of gear A (rA) = 250mm
Radius of gear B (rB) = 250mm
Radius of gear C (rC) = 100mm
Calculation:
Moment of inertia of gear A
Moment of inertia of gear B
Moment of inertia of gear C
For Initial condition;
Angular velocity of the gear C is 450 rpm,
Gear C mess with Gear A. So angular velocity ration is given as
Gear C mess with gear B
Initial kinetic energy
For final condition; Angular velocity of the gear C is 1800rpm
Gear C mess with Gear A. So angular velocity ration is given as
Gear C mess with gear B
Final kinetic energy
Work done by the gear C
Substitute the value of E1, E2 and W in work energy equation
(b)
Tangential force on gear A.
Answer to Problem 17.11P
Tangential force on gear A is F = 0.0447N.
Explanation of Solution
Given information:
Mass of the gear A (mA) = 10kg.
Radius of gyration of the gear A (kA) = 190mm.
Mass of the gear B (mB) = 10kg.
Radius of gyration of the gear B (kB) = 190mm.
Mass of the gear C (mC) = 2.5kg.
Radius of gyration of the gear C (kC) = 80mm.
Initial angular velocity of gear C (Nc)1 = 450rpm
Final angular velocity of gear C (NC)1 = 1800rpm
A couple at gear C (M) = 6N-m.
Radius of gear A (rA) = 250mm
Radius of gear B (rB) = 250mm
Radius of gear C (rC) = 100mm
Calculation:
Angle of rotation for gear A
Substitute the value of E1, E2 and W in work energy equation for gear A
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Chapter 17 Solutions
Vector Mechanics For Engineers
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